Questions tagged [quantum-chemistry]

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Why do all atoms follow the same $n$ and $\ell$ quantization conditions as hydrogen? [duplicate]

The quantum state of an electron in a hydrogen atom is specified by 4 quantum numbers: $n$ , $\ell$, $m_\ell$, $m_s$ which can take the following values: $$n = 1, 2, 3, ... $$ $$\ell = 0, 1, 2, 3, ......
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Can Hartree-Fock-Bogoliubov be used for dynamics?

I am aware of Hartree-Fock as both a tool to find interacting ground states for fermionic systems (eg the Roothan self-consistent field procedure). One way of deriving the ground state method is to ...
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What (in silico information) defines the transfer function of a Quantum Amplifier, in the form of a molecule?

Let’s say a team of scientists have published the structure of a molecule they claim acts as a quantum amplifier. Photons travel along a quantum channel carrying qubits in their polarization. The ...
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On diagonal terms in the Coulomb matrix

I have seen many machine learning algorithms for prediction of quantum chemistry properties that use Coulomb matrix as their input. Coulomb matrix is defined as $$\boldsymbol{M}_{i j}^{\mathrm{...
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Calculating Simple Ground State Energy Of Hydrogen From Geminal Spin Function

I'm very new to quantum stuff and I'm experimenting, but I'd like a good explanation here if you can give it. Here's the circuit diagram and the results. I'm seeing from this paper that you can get ...
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25 views

What exactly does it mean for an element to experimentally violate the Madelung ordering rule?

The Madelung ordering rule says that as you increase the atomic number of a neutral atom, the electron orbitals fill up in order of increasing value of $n+l$, and in increasing order of $n$ within a ...
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1answer
78 views

What is $\frac{d}{d\psi}\langle\psi| \hat{O} | \psi\rangle$?

I would like to know what is the derivative of an expectation value with respect to the molecular state $$\frac{d}{d\psi}\langle\psi| \hat{\mathbf{O}} | \psi\rangle$$ Note that here $|\psi\rangle$ ...
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42 views

The overlap of two Slater determinant states

Suppose I have two fermionic number states in different bases, with the same particle number $N$ - call them $|\Psi\rangle$ and $|\Phi\rangle$. In the position basis, I can write the many-body ...
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How can I obtain by hand the molecular orbital expression for the H2 system, using the Self Consistent Field (SCF) Cycle in DFT calculations?

After doing some energy calculations for the H2 system in Gaussian, using wb97xd/STO-3G basis, and generating a .wfn file, I wanted to understand better how the computer does the calculations. I ...
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23 views

In what cases do isotopes cause non-negligible effects in chemicals

For example, CO2 (carbon dioxide), there could be Carbon8-Carbon22 isotopes, and I'm not sure for oxygen. Wondering at what point there is some sort of non-negligible effect, and what the effect(s) ...
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Band formation in diamond

Why is it that in the band diagram of diamond does the sp3 hybridised orbital split into two forming valence band and conduction band? I thought that these sp3 hybridised orbital forms 4n bonding and ...
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What is a nuclear wave packet?

What is the definition of a nuclear wave packet ? I often see the term used but i don't know how it is defined. It seems to be connected to the Born-Oppenheimer approximation. Is it defined there and ...
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Branch of Physics that Examines Atoms Relationships

Is there a specific branch of physics that can examine and calculate the strengths of atomic or molecular bonds and predict how they are going to break, putting into consideration the surrounding ...
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67 views

What's meaning of velocity of electron? [closed]

How do we define velocity of microscopic particles at small scales. As for macroscopic particle we can scale the distance travelled by object. But this is not the case with electron. Still, while ...
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2answers
79 views

What is the simplest possible Hamiltonian that yields an Antisymmetric Wavefunction?

I am using a Split-Operator Fourier Transform (SOFT) technique to solve the time-dependent electronic Schrödinger Equation (TDSE) for a Hydrogen molecule under the Born-Oppenheimer approximation. So I ...
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12 views

Proof that Restricted Open-shell Hartree–Fock can not take the canonical form

In Frank Jensen's Introduction to Computational Chemistry ($\mathrm{2^{nd}}$ edition), on page 99, it says: For an ROHF wave function, it is not possible to choose a unitary transformation that ...
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1answer
150 views

$sp^3$ Hybridization wavefunctions and probability density

I have plotted a hydrogen-like sp3-hybrid orbital probability density and it looks like this: I can plot 4 overlapping probability densities in a tetrahedral shape: So far it looks OK. But when I'm ...
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1answer
97 views

1D Infinite Square Well: Box Suddenly Increase in Size. Why the coefficients can be derived by inner producting the wave functions?

I have read the question 1D Infinite Square Well: Box Suddenly Increase in Size. How treat this?. There are two key equations in the selected answer. $$\int_0^{2L} dx \ \psi^*_m\left(x\right) \Psi\...
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2answers
60 views

Basis Functions for Hartree Fock, and Configuration Interaction

I'm about halfway through the book Szabo and Ostlund, and while I think I understand the rough idea of Hartree-Fock and configuration interaction, there is something I would like to clarify. For one, ...
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21 views

Program for calculating transition amplitudes

I calculated transition amplitudes with MBPT analytically and used Slater-Condon rules. Now I have a very long expression and I would like to solve my matrix elements. Does someone know a program for ...
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Operator for change of state?

I am trying to model a quantum system that has only three different classical states, so that the Hilbert space is simply $\mathbb C^3$, and let's call its standard basis $e_1,e_2,e_3$, with each of ...
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68 views

Direction of the permanent dipole moment of the NH$_3$ molecule

What is the direction of dipole moment in a molecule of $\rm NH_3$? Is from hydrogen to nitrogen? Also do we take into account the dipole moment of the lone pair with hydrogen? When we must take into ...
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1answer
67 views

How to propagate Heller's model of the Gaussian Wave Packet? [closed]

I'm working on an undergraduate research project on gaussian wave packets, but am a pretty big noob in terms of theoretical chemistry and the like. I'm having a lot of difficulty grasping this concept ...
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19 views

Bond Type in Orthophosphate

How can we find out the bond nature in LiBaPO4 by using charge transfer values obtained through DFT calculations?
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375 views

Would an $H_2O$ Molecule actually look like this 3D representation if we could see it?

I'm trying to get a much better grasp on atoms and molecules and I am a visual learner. I found the above image here. This intuitively makes sense to me because I can see how the electron orbitals ...
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2answers
50 views

Sign of exchange integral in quantum chemistry?

I have a question about exchange integral in quantum chemistry. Usually, we learn that the sign of exchange integral is positive, so a triplet state has lower energy than singlet state. Is it ...
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76 views

What is the energy of an atomic orbital?

When we refer to energy of an atomic orbital what is this energy ? is potential energy ? but if is potential energy then shouldn't be considered the whole potential energy of the atom ( potential ...
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1answer
273 views

Putting high symmetry points labels to a band structure plot [closed]

So far I've got this plot using Quantum Espresso. I want to put gamma, X, L, etc labels to the k-path. Quantum Espresso's ouput states the following: ...
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1answer
69 views

What are some molecular systems which have quantum states that are measurably incompatible?

What I'm looking for is a molecular system, which we can produce in a lab, that is, A discrete variable system (ie, a finite dimensional hilbert space) It has observables that are incompatible with ...
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41 views

Electronic configuration

In chemistry the lithium electronic configuration is $$1s^22s^1 \, .$$ Can we prove this using approximation method like perturbation theory that this the ground state and not for example $1s^22p^...
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51 views

How to determine symmetry of the system from the term symbol?

I'm studying term symbols. I can derive them mechanically from the electron configuration using the complete table of microstates. Let's consider a typical example - an atomic carbon with the ...
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28 views

In what cases (precisely) are Hund's rules valid?

I can't find on any good source (such as a textbook) a precise specification about the cases when Hund's rules (especially Hund's third rule) for an electronic configuration of atom are valid (the ...
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1answer
48 views

Planck blackbody radiation

I am reading a chapter about blackbody radiation in my physics textbook, and I encountered the following equation: $$d\rho(\nu, T)=\rho_\nu(T)d\nu=\frac{8\pi k_BT}{c^3}\nu^2d\nu$$ which is a classical ...
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1answer
51 views

Reference request for symmetry breaking Hartree-Fock

Stationary mean-field solutions break symmetries of the many-body Hamiltonian in favour of lowering the energy, e.g. translational or rotational symmetry, despite $[H,P]=0$, or $[H,L_z]=0$, ...
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What would measuring the position of an electron in an electronic superposition look like?

In view of the Copenhagen interpretation, the state: $$\Psi = \frac{1}{\sqrt{2}}|0⟩ + \frac{1}{\sqrt{2}}|1⟩$$ is interpreted as "when the system is measured, you have a 50% chance of finding the ...
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55 views

How do I proceed with the following coulomb integral?

I am trying to solve the $H_{2}^{+}$ ion problem using Fourier transform approach. The Hamiltonian that I am trying to solve is as follows, $$H=-\frac{\hbar^{2}}{2m_{e}}\nabla^{2}_{e}-\frac{e^{2}}{4\...
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1answer
66 views

How to explain about Raman spectroscopy?

What is the definition of Raman spectroscopy? How to explain in brief about antistoke line and Stoke line and Rayleigh?
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111 views

What is orthogonalization energy when two atoms overlap?

In this paper, I read that: When two atoms overlap, quantum mechanics dictates that they be orthogonal to each other. This drives up the energy and leads to so-called Pauli exclusion. The amount of ...
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Is there a mathematical singularity in the relativistic contraction of valence orbitals as a function of nuclear charge?

I'm looking at Figure 1 on p. 2 of Jansen, "Effects of relativistic motion of electrons on the chemistry of gold and platinum" (2005) (should be a free download). From the bottom curve, there is such ...
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Do relativistically-contracted electron states have the same energy and angular momentum values?

I've been reading that electron bound states are defined by four quantum numbers, $n$, $l$, $m_l$, and $m_s$, respectively the principal quantum number, the azimuthal quantum number, the magnetic ...
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1answer
210 views

How can I do quantum chemistry with QED?

So I am a theoretical and computational chemist by trade and my usual zone of operation in the domain of quantum mechanics is Hartree-Fock and Density Functional Theories. I was thinking if there ...
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1answer
166 views

How exact are the Kadanoff-Baym equations?

In a General nonequilibrium Quantum chemical System, the Kadanoff-Baym equations have the form: $(i \partial_t -h_2-\Sigma_{H,2})G_<(1,2) = \delta_C(1, 2) + \int d3 \Sigma (1,3)G_<(3,2)$ where ...
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Stability of saturated energy levels

In The Feynman Lectures on Physics, Vol. 3, Section 15-5, there's a discussion of the stability of various benzene ions. It turns out that the ions for which the all the energy levels up to a certain ...
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1answer
51 views

Can diffusion occur without thermal motion of molecules?

If I would ask: What are the Basic mechanisms of diffusion? I would get the answer: Because of thermal Brownian Motion. But are there other causes besides Brownian motion for Diffusion? Can ...
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1answer
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Is the Hartree-Fock approximation getting better and better for higher atoms?

As the atomic number $Z$ increases, is the Hartree-Fock approximation getting better and better, or worse and worse?
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34 views

Does a Conical Intersection imply that the HOMO-LUMO gap in a molecule is very small?

I came across some notes in which the author swiftly made this comment, that if there's always a large gap between the HOMO and the LUMO along a chemical reaction ("large" can mean at least bigger ...
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many-body problems and why they are so hard

I am currently reading my first course in electronic structure theory and i have questions relating to the complexity of the many-body Schrödinger equation for quantum chemistry. More precisely about ...
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How can special relativity account for the electron orbital clouds of (stationary) heavy elements when electrons don't orbit in a classical way?

Einstein's famous mass-energy equivalence equation is still used for calculations, but still often considered less physically meaningful since the atoms that comprise a material don't actually gain ...
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Significance of ground state energy in quantum chemistry

I'm reading a paper that says "The fundamental goal in electronic-structure problems is to solve for the ground-state energy of many-body interacting fermionic Hamiltonians" (ref: https://arxiv.org/...
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1answer
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Pi-bond angular momentum

I quantum chemistry literatute one can find a statement about projection of the angular momentum on internuclear axis: The angular momentum vector for rotation about the bond will lie along the ...